Multi-Objective Optimization Design of Ring-Shaped CX-ABH Plate for Vibration Reduction and Energy Concentration

The acoustic black hole (ABH) effect, achieved through a power-law thickness profile, has emerged as a powerful technique for passive vibration and noise control in thin-walled structures by slowing and trapping bending waves. However, prevailing research and designs predominantly focus on concave ABH indentations, which inherently require material removal and can consequently compromise structural strength and load-bearing capacity. To overcome this limitation, this paper introduces a novel symmetrical ring-shaped convex acoustic black hole (CX-ABH) plate. This innovative configuration transitions from the conventional concave geometry to a convex profile, aiming to preserve or even enhance vibration reduction performance while simultaneously improving structural integrity. A finite element model of the proposed ring-shaped CX-ABH plate is established and its calculation accuracy has been numerically validated through mesh independence testing. Vibration response analyses demonstrate its superior performance against a baseline rectangular plate at approximately 1270 Hz, achieving a maximum vibration reduction of 28.26 dB; the kinetic energy density is decreased by up to 2.82 J/m3 and effective energy concentration is achieved within the CX-ABH region. A parametric study was conducted to investigate the influence of key geometric parameters: the ABH radius R, the power exponent m, and the central frustum radius d. To achieve an optimal design, a Kriging surrogate model is constructed based on simulation data and subsequently coupled with a multi-objective genetic algorithm (MOGA) for systematic optimization. The derived optimal parameter set (d = 13.5 mm, m = 2.4, R = 58.9 mm) yields a 16.53% reduction in the mean peak kinetic energy density, validating the effectiveness of the optimization framework. The results conclusively demonstrate that the ring-shaped CX-ABH plate offers a promising and novel structural paradigm, successfully balancing high-efficiency broadband vibration attenuation with a robust structural design.